NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions
Question 68

Question. 68

Open your geometry box. There are some drawing tools. Observe them and complete the following table:

Name of the toolNumber of lines of symmetry
(i) The Ruler_____
(ii) The Divider_____
(iii) The Compasses_____
(iv) The Protractor_____
(v) Triangular piece with two equal sides_____
(vi) Triangular piece with unequal sides_____

Answer:

Name of the toolNumber of lines of symmetry
(i) The Ruler2
(ii) The Divider1
(iii) The Compasses0
(iv) The Protractor1
(v) Triangular piece with two equal sides1
(vi) Triangular piece with unequal sides0

Detailed Answer with Explanation:

Explanation — Lines of Symmetry (Very Beginner-Friendly)

What is a line of symmetry?

( ext{A line of symmetry divides a shape into two mirror halves.})

( ext{After folding on that line, both halves match exactly.})


  1. (i) The Ruler (think of it as a rectangle)

    ( ext{A rectangle has a vertical symmetry line through its center.})

    ( ext{It also has a horizontal symmetry line through its center.})

    Therefore: 2 lines of symmetry (ignore the printed markings).

  2. (ii) The Divider (two equal arms joined at a hinge)

    ( ext{When both arms are opened equally, there is one middle line.})

    ( ext{This middle line is the angle bisector and acts as symmetry.})

    Therefore: 1 line of symmetry.

  3. (iii) The Compasses (one arm has a pencil, the other a needle)

    ( ext{The two arms are not identical.})

    ( ext{No fold can make both sides match perfectly.})

    Therefore: 0 lines of symmetry.

  4. (iv) The Protractor (a standard 180° semicircle with a straight base)

    ( ext{There is one line through the center, perpendicular to the base.})

    ( ext{This line splits the semicircle into two equal mirror parts.})

    Therefore: 1 line of symmetry.

  5. (v) Triangular piece with two equal sides (an isosceles triangle)

    ( ext{The line from the top vertex to the midpoint of the base})

    ( ext{splits the triangle into two equal halves.})

    Therefore: 1 line of symmetry.

  6. (vi) Triangular piece with unequal sides (a scalene triangle)

    ( ext{All sides and angles are different.})

    ( ext{No fold can make both halves match.})

    Therefore: 0 lines of symmetry.


Quick check: ruler = 2, divider = 1, compasses = 0, protractor = 1, isosceles set-square = 1, scalene triangle = 0.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – Problems and Solutions | Detailed Answers